OK. To be fair.. most of these poses are designed to open the hips, which should prepare the body for labor but not necessarily "induce" it.. but people say squats particularly and hip openers might help if you're at term and ready to go. (I am!)
See also Dear Baby
Without further ado, I give you 5 Poses That Should Induce Labor (But Don't Work If You're Me Because My Baby Doesn't Want to Come Out and I'm Going to Be Pregnant Forever)
1. Malasana (Garland Pose)
2. Goddess Pose.
3. Prasarita Padottanasana (Wide Legged Forward Bend).
4. Baddha Konasana (Cobblers Pose) while pressing the "trigger point" between your ankle bone and heel.
5. Parivrtta Surya Yantrasana (Compass Pose). A milder modified version of this to open my hips.
Other things that don't work...
Bouncing on a Yoga Ball
Not yet tested...
See also ...
What Not to Wear: Yoga Mamas
Baby Yoga? This is How We Do It
6 Reasons Every Mama Needs a Yoga Ball
3 Surprising Reasons Every Mama Needs a Yoga Mat